Question: All of the 3rd grade teachers and students from Oak went on a field trip to an art museum. Tickets were $$6.00$ each for teachers and $$4.50$ each for students, and the group paid $$39.00$ in total. The next month, the same group visited a natural history museum where the tickets cost $$18.00$ each for teachers and $$9.50$ each for students, and the group paid $$93.00$ in total. Find the number of teachers and students on the field trips.
Answer: Let $x$ equal the number of teachers and $y$ equal the number of students. The system of equations is: ${6x+4.5y = 39}$ ${18x+9.5y = 93}$ Solve for $x$ and $y$ using elimination. Multiply the top equation by $-3$ ${-18x-13.5y = -117}$ ${18x+9.5y = 93}$ Add the top and bottom equations together. $ -4y = -24 $ $ y = \dfrac{-24}{-4}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $ {6x+4.5y = 39}$ to find $x$ ${6x + 4.5}{(6)}{= 39}$ $6x+27 = 39$ $6x = 12$ $x = \dfrac{12}{6}$ ${x = 2}$ You can also plug ${y = 6}$ into $ {18x+9.5y = 93}$ and get the same answer for $x$ ${18x + 9.5}{(6)}{= 93}$ ${x = 2}$ There were $2$ teachers and $6$ students on the field trips.